How to Use Simulink

8/12/2019 How to Use Simulink

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Simulink Basics Tutorial

Simulink is a graphical extension to MATLABfor modeling and simulation of systems. In

Simulink, systems are drawn on screen as block diagrams. Many elements of blockdiagrams are available, such as transfer functions, summing junctions, etc., as well as

virtual input and output devices such as function generators and oscilloscopes. These

virtual devices will allow you to perform simulations of the models you will build.Simulink is integrated with MATLABand data can be easily transferred between the

programs. In this tutorial, we will apply Simulink to the examples of modeled systems,

then build controllers, and simulate the systems

Starting Simulink

Simulink is started from the MATLABcommand prompt by entering the following

command:

si mul i nk

Alternatively, you can hit the New Simulink Model button at the top of the MATLABcommand window as shown below:

When it starts, Simulink brings up two windows. The first is the main Simulink window,

which appears as shown or similar to this as different versions of the software are found:


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The second window is a blank, untitled, model window. This is the window into which anew model can be drawn.

Model Files

In Simulink, a model is a collection of blocks which, in general, represents a system. In

addition, to drawing a model into a blank model window, previously saved model filescan be loaded either from the Filemenu or from the MATLAB command prompt. As a

first exercise we will be building a model.

You can open a file in Simulink by entering the following command in the MATLAB

command window. (Alternatively, you can load this file using the Openoption in theFilemenu in Simulink, or by hitting Ctrl+O in Simulink.)

Fi l e name. mdl

For our purposes we will create the following model in simulink. A new model can be

created by selecting Newfrom the Filemenu in any Simulink window (or by hitting

Ctrl+N). Using the information below, create the following model.

Basic Elements

There are two major classes of items in Simulink: blocksand lines. Blocks are used to

generate, modify, combine, output, and display signals. Lines are used to transfer signalsfrom one block to another.


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Blocks

There are several general classes of blocks:

Sources: Used to generate various signals Sinks: Used to output or display signals Discrete: Linear, discrete-time system elements (transfer functions, state-space

models, etc.)

Linear: Linear, continuous-time system elements and connections (summingjunctions, gains, etc.)

Nonlinear: Nonlinear operators (arbitrary functions, saturation, delay, etc.) Connections: Multiplex, Demultiplex, System Macros, etc.

Blocks have zero to several input terminals and zero to several output terminals. Unused

input terminals are indicated by a small open triangle. Unused output terminals are

indicated by a small triangular point. The block shown below has an unused input

terminal on the left and an unused output terminal on the right.

Lines

Lines transmit signals in the direction indicated by the arrow. Lines must always transmit

signals from the output terminal of one block to the input terminal of another block. Onexception to this is a line can tap off of another line, splitting the signal to each of two

destination blocks, as shown. Lines can never inject a signal intoanother line; lines mustbe combined through the use of a block such as a summing junction.

A signal can be either a scalar signal or a vector signal. For Single-Input, Single-Output

systems, scalar signals are generally used. For Multi-Input, Multi-Output systems, vectorsignals are often used, consisting of two or more scalar signals. The lines used to transmit

scalar and vector signals are identical. The blocks on either end of the line determine the

type of signal carried by the line.


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Simple Example

The simplemodel (from the model filesection) consists of three blocks: Step, TransferFcn, and Scope. The Step is a source blockfrom which a step input signal originates.

This signal is transferred through the linein the direction indicated by the arrow to the

Transfer Function linear block. The Transfer Function modifies its input signal andoutputs a new signal on a line to the Scope. The Scope is a sink blockused to display a

signal much like an oscilloscope.

There are many more types of blocks available in Simulink, some of which will be

discussed later. Right now, we will examine just the three we have used in the simple

model.

Modifying Blocks

A block can be modified by double-clicking on it. For example, if you double-click on

the "Transfer Fcn" block in the simplemodel, you will see the following dialog box.

This dialog box contains fields for the numerator and the denominator of the block's

transfer function. By entering a vector containing the coefficients of the desirednumerator or denominator polynomial, the desired transfer function can be entered. For

example, to change the denominator to s^2+2s+1, enter the following into the

denominator field:[ 1 2 1]
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and hit the close button, the model window will change to the following,

which reflects the change in the denominator of the transfer function.

The "step" block can also be double-clicked, bringing up the following dialog box.

The default parameters in this dialog box generate a step function occurring at time=1

sec, from an initial level of zero to a level of 1. (in other words, a unit step at t=1). Each

of these parameters can be changed. Close this dialog before continuing.

The most complicated of these three blocks is the "Scope" block. Double clicking on this

brings up a blank oscilloscope screen.

When a simulation is performed, the signal which feeds into the scope will be displayed


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in this window. Detailed operation of the scope will not be covered in this tutorial. The

only function we will use is the autoscale button, which appears as a pair of binoculars in

the upper portion of the window.

Running Simulations

To run a simulation, we will work with the following model. Using the techniques

developed above creates the following model:

Before running a simulation of this system, first open the scope window by double-

clicking on the scope block. Then, to start the simulation, either select Startfrom theSimulationmenu (as shown below) or hit Ctrl-T in the model window.

The simulation should run very quickly and the scope window will appear as shown

below.

Note that the simulation output (shown in yellow) is at a very low level relative to the


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axes of the scope. To fix this, hit the autoscale button (binoculars), which will rescale the

axes as shown below.

Note that the step response does not begin until t=1. This can be changed by double-clicking on the "step" block. Now, we will change the parameters of the system andsimulate the system again. Double-click on the "Transfer Fcn" block in the model

window and change the denominator to[ 1 20 400]

Re-run the simulation (hit Ctrl-T) and you should see what appears as a flat line in the

scope window. Hit the autoscale button, and you should see the following in the scope

window.

Notice that the autoscale button only changes the vertical axis. Since the new transferfunction has a very fast response, it compressed into a very narrow part of the scopewindow. This is not really a problem with the scope, but with the simulation itself.

Simulink simulated the system for a full ten seconds even though the system had reached

steady state shortly after one second.

To correct this, you need to change the parameters of the simulation itself. In the modelwindow, select Parametersfrom the Simulationmenu. You will see the following


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dialog box.

There are many simulation parameter options; we will only be concerned with the start

and stop times, which tell Simulink over what time period to perform the simulation.Change Start timefrom 0.0 to 0.8 (since the step doesn't occur until t=1.0. Change Stop

timefrom 10.0 to 2.0, which should be only shortly after the system settles. Close the

dialog box and rerun the simulation. After hitting the auto-scale button, the scopewindow should provide a much better display of the step response as shown below.

Building Systems

In this section, you will learn how to build systems in Simulink using the building blocksin Simulink's Block Libraries. You will build the following system.
http://e/ctmssimulinkbasicblocklib.htmhttp://e/ctmssimulinkbasicblocklib.htm


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First you will gather all the necessary blocks from the block libraries. Then you willmodify the blocks so they correspond to the blocks in the desired model. Finally, you will

connect the blocks with lines to form the complete system. After this, you will simulatethe complete system to verify that it works.

Gathering Blocks

Follow the steps below to collect the necessary blocks:

Create a new model (Newfrom the Filemenu or Ctrl-N). You will get a blankmodel window.


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Double-click on the Sources icon in the main Simulink window.

This opens the Sources window which contains the Sources Block Library.

Sources are used to generate signals. Click herefor more information on blocklibraries.
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Drag the Step block from the sources window into the left side of your modelwindow.

Double-click on the Linear icon in the main Simulink window to open the LinearBlock Library window.

Drag the Sum, Gain, and two instances of the Transfer Fcn (drag it two times)into your model window arranged approximately as shown below. The exact

alignment is not important since it can be changed later. Just try to get the correct

relative positions. Notice that the second Transfer Function block has a 1 after itsname. Since no two blocks may have the same name, Simulink automatically

appends numbers following the names of blocks to differentiate between them.

Double-click on the Sinks icon in the main Simulink window to open the Sinkswindow.


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Drag the Scope block into the right side of your model window.

Modify Blocks

Follow these steps to properly modify the blocks in your model.

Double-click your Sum block. Since you will want the second input to besubtracted, enter +- into the list of signs field. Close the dialog box.

Double-click your Gain block. Change the gain to 2.5 and close the dialog box. Double-click the leftmost Transfer Function block. Change the numerator to [1 2]

and the denominator to [1 0]. Close the dialog box.

Double-click the rightmost Transfer Function block. Leave the numerator [1], butchange the denominator to [1 2 4]. Close the dialog box. Your model should

appear as:

Change the name of the first Transfer Function block by clicking on the words"Transfer Fcn". A box and an editing cursor will appear on the block's name as

shown below. Use the keyboard (the mouse is also useful) to delete the existingname and type in the new name, "PI Controller". Click anywhere outside the


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name box to finish editing.

Similarly, change the name of the second Transfer Function block from "TransferFcn1" to "Plant". Now, all the blocks are entered properly. Your model should

appear as:

Connecting Blocks with Lines

Now that the blocks are properly laid out, you will now connect them together. Follow

these steps.

Drag the mouse from the output terminal of the Step block to the upper (positive)input of the Sum block. Let go of the mouse button only when the mouse is righton the input terminal. Do not worry about the path you follow while dragging, the

line will route itself. You should see the following.


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The resulting line should have a filled arrowhead. If the arrowhead is open, asshown below, it means it is not connected to anything.

You can continue the partial line you just drew by treating the open arrowhead asan output terminal and drawing just as before. Alternatively, if you want toredraw the line, or if the line connected to the wrong terminal, you should delete

the line and redraw it. To delete a line (or any other object), simply click on it to

select it, and hit the delete key.

Draw a line connecting the Sum block output to the Gain input. Also draw a linefrom the Gain to the PI Controller, a line from the PI Controller to the Plant, and a


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line from the Plant to the Scope. You should now have the following.

The line remaining to be drawn is the feedback signal connecting the output of thePlant to the negative input of the Sum block. This line is different in two ways.

First, since this line loops around and does not simply follow the shortest (right-

angled) route so it needs to be drawn in several stages. Second, there is no outputterminal to start from, so the line has to tap off of an existing line.

To tap off the output line, hold the Ctrl key while dragging the mouse from the

point on the existing line where you want to tap off. In this case, start just to the

right of the Plant. Drag until you get to the lower left corner of the desiredfeedback signal line as shown below.

Now, the open arrowhead of this partial line can be treated as an output terminal.


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Draw a line from it to the negative terminal of the Sum block in the usual manner.

Now, you will align the blocks with each other for a neater appearance. Onceconnected, the actual positions of the blocks does not matter, but it is easier to

read if they are aligned. To move each block, drag it with the mouse. The lineswill stay connected and re-route themselves. The middles and corners of lines can

also be dragged to different locations. Starting at the left, drag each block so thatthe lines connecting them are purely horizontal. Also, adjust the spacing between

blocks to leave room for signal labels. You should have something like:

Finally, you will place labels in your model to identify the signals. To place alabel anywhere in your model, double click at the point you want the label to be.

Start by double clicking above the line leading from the Step block. You will get ablank text box with an editing cursor as shown below


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Type an r in this box, labeling the reference signal and click outside it to endediting.

Label the error (e) signal, the control (u) signal, and the output (y) signal in thesame manner. Your final model should appear as:

To save your model, select Save Asin the Filemenu and type in any desiredmodel name. The completed model can be found here.

Simulation

Now that the model is complete, you can simulate the model. Select Startfrom the

Simulationmenu to run the simulation. Double-click on the Scope block to view its
http://e/ctmssimulinkbasicbuildex.mdlhttp://e/ctmssimulinkbasicbuildex.mdl


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output. Hit the autoscale button (binoculars) and you should see the following.

Taking Variables from MATLAB

In some cases, parameters, such as gain, may be calculated in MATLABto be used in a

Simulink model. If this is the case, it is not necessary to enter the result of the MATLAB

calculation directly into Simulink. For example, suppose we calculated the gain inMATLABin the variable K. Emulate this by entering the following command at the

MATLABcommand prompt.K=2. 5

This variable can now be used in the Simulink Gain block. In your simulink model,

double-click on the Gain block and enter the following in the Gain field.K

Close this dialog box. Notice now that the Gain block in the Simulink model shows the

variable K rather than a number.


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Now, you can re-run the simulation and view the output on the Scope. The result shouldbe the same as before.

Now, if any calculations are done in MATLABto change any of the variable used in the

Simulink model, the simulation will use the new values the next time it is run. To try this,

in MATLAB, change the gain, K, by entering the following at the command prompt.K=5


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Start the Simulink simulation again, bring up the Scope window, and hit the auto-scale

button. You will see the following output which reflects the new, higher gain.

Besides variable, signals, and even entire systems can be exchanged between MATLAB

and Simulink. For more information see below

Simulink Basics Tutorial - Interaction With

MATLABDefining Block Parameters Using MATLABVariables

Exchanging Signals With MATLAB

Extracting Models From Simulink Into MATLAB

We will examine three of the ways in which Simulink can interact with MATLAB.

Block parameters can be defined from MATLABvariable. Signals can be exchanged between Simulink and MATLAB. Entire systems can be extracted from Simulink into MATLAB.

Block Parameters from MATLABVariables

Often, a controller will be designed in MATLABand verified in a Simulink model.

Normally, numerical parameters such as gains and controller transfer functions areentered into simulink manually by entering the numbers in the block dialog boxes. Rather
http://e/ctmssimulinkbasic%22%20lhttp://e/ctmssimulinkbasic%22%20lhttp://e/ctmssimulinkbasic%22%20lhttp://e/ctmssimulinkbasic%22%20lhttp://e/ctmssimulinkbasic%22%20lhttp://e/ctmssimulinkbasic%22%20lhttp://e/ctmssimulinkbasic%22%20lhttp://e/ctmssimulinkbasic%22%20lhttp://e/ctmssimulinkbasic%22%20lhttp://e/ctmssimulinkbasic%22%20l


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than enter numbers directly, it is possible to use MATLABvariable in Simulink block

dialog boxes.

For example, bring up the Simulink modelbuilt in the Basics tutorial(or click heretodownload it.)

In this case, the complete controller transfer function is:

s+22. 5 - - - - -

s

Suppose this transfer function were generated by some computation in MATLAB. In this

case, there would most likely be three variable, the numerator polynomial, thedenominator polynomial, and the gain. Enter the following commands in MATLABto

generate these variable.K=2. 5num=[ 1 2]

den=[ 1 0]These variable can now be used in the blocks in Simulink. In your simulink model,

double-click on the Gain block. Enter the following in the Gain field.

K

Close this dialog box. Notice now that the Gain block in the Simulink model shows the

variable K rather than a number.
http://e/ctmssimulinkbasicbasic.htmhttp://experiment%20/#1%20-%20Matlab%20&%20Simulink%20Tutorialhttp://experiment%20/#1%20-%20Matlab%20&%20Simulink%20Tutorialhttp://e/ctmssimulinkbasicbasic.htm


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Double-click on the PI Controller block. Enter the following into the Numerator field.

num

Enter the following into the Denominator field.den

Close this dialog box. Notice now that the PI Controller block shows the variable numand den (as functions of s) rather than an explicit transfer function.


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You can simulate the model with the MATLABvariable parameters. Select Startfrom the

Simulationmenu to run the simulation. Double-click on the Scope block to view itsoutput. Hit the autoscale button (binoculars) and you should see the following.

Now, if any calculations are done in MATLABto change any of the variable used in theSimulink model, the simulation will use the new values the next time it is run. To try this,

in MATLAB, change the gain, K, by entering the following at the command prompt.K=5

Start the Simulink simulation again, bring up the Scope window, and hit the autoscale

button. You will see the following output which reflects the new, higher gain.

To download the model with MATLABvariable parameters, click here.

Exchanging Signals with MATLAB

Sometimes, we would like to use the results of a Simulink simulation in the MATLABcommand window for further calculations and plotting. Less often, we would like to

generate signals in MATLABwhich we then use as inputs in a Simulink model. These

tasks are accomplished through the use of the To Workspace Sink Block and the From
http://e/ctmssimulinkbasicvariab.mdlhttp://e/ctmssimulinkbasicvariab.mdl


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Workspace Source Block. We will only transfer signals from Simulink to MATLAB.

Doing the reverse is a very similar process.

The To Workspace Sink Block saves a signal as a vector in the MATLABWorkspace.Open the model which you used previously in this tutorial or click hereto download the

model. Be sure that the variable K (=5), num (=[1 2]), and den (=[1 0]) are defined inMATLAB.

Supposewe would like to use both the output signal and the control signal for calculations in

MATLAB. We will save these two variables as well as a time signal from our Simulinkmodel. First, you need to generate a time signal. Open the Sources window by double-

clicking the Sources icon in the main Simulink window. Drag the Clock block from the

Sources window to the lower portion of your Simulink model.

Now, open the Sinks window and drag three instances of the To Workspace block to yourSimulink window, arranged approximately as shown below.
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Before connecting these blocks to the rest of your system, first you will name the variableto which they output. The lower To Workspace block will output the time signal to the

MATLABvariable. Double-click on this block and enter the following in the Variable

Name field.

t

Close the dialog box. Notice that the lower To Workspace block shows a t.


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Start the simulation (Startfrom the Simulationmenu). You can still view the output inthe Scope window (remember autoscale).

You can now examine the outputted variable in the MATLABwindow. Plot u and y vs. t

by entering the following command.pl ot ( t , u, t , y) ;

Note that it is important to plot each of these variables against the time vector generated

by Simulink, since the time between elements in the signal vectors u and y may be

unequal, particularly near a discontinuity such as the step input. Your plot of u (blue) andy (green) should appear as follows.


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To download the model with outputs to MATLABvariable, click here.

Extracting Models From Simulink into MATLAB

Sometimes, we may build a complicated model in simulink and would like to derive

either a transfer function or a state space model of the entire system. In order to do this,

you first need to define the input and output signals of the model to be extracted. Thesevirtual signals can be any signal in a model, for example, if we can generate an input-to-

output transfer function or a disturbance-to-error transfer function. These signals are

defined using the In and Out Connection Blocks.

Once the input/output model is defined, the Simulink model must be saved to a .mdl file.

This file is then referenced in the MATLABcommand window by the linmodcommand.

To demonstrate this, bring up your model from the previous section of this tutorial (or

click hereto download it). Be sure that the variable K (=5), num (=[1 2]), and den (=[1

0]) are defined in MATLAB.
http://e/ctmssimulinkbasicoutvar.mdlhttp://e/ctmssimulinkbasicoutvar.mdlhttp://e/ctmssimulinkbasicoutvar.mdlhttp://e/ctmssimulinkbasicoutvar.mdl


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You will be extracting a closed-loop reference-to-output model. Therefore, The virtualinput will be put in place of the step input to the system. First, delete the Step block (click

on it and hit the delete key). The previous line will remain with an open input terminal

where it used to connect to the Step. Open the Connections window from the mainSimulink window. Drag an In Block from the Connections window to your model

window in place of the Step block you just deleted. Move the In block until the output

terminal of the In block touches the open input terminal of the left over line. The lineshould attach to the In block.

The virtual output does not need to replace an existing block - the signal can be tappedoff an existing line. Drag an Out block from the Connections window and place it just

above the Scope block. Tap a line off the output signal (hold Ctrl) and connect it to the

out block.


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Now, save this model under a new name. Call it mymodel.mdl. You can download a

version here.

At the MATLABprompt, enter the following command to extract a state-space modelfrom your model file.

[ A, B, C, D] =l i nmod( ' mymodel ' )

You should see the following output.A =

- 2 - 9 21 0 00 - 5 0

B =

505

C =

0 1 0

D =

0

This can, of course, be converted to a transfer function with the following command.[ numcl , dencl ] =ss2t f ( A, B, C, D)

You should get the following output.numcl =

0 0 5. 0000 10. 0000

dencl =
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1. 0000 2. 0000 9. 0000 10. 0000

To verify that the model transfered properly, you can obtain a step response of the

extracted model.st ep( numcl , dencl )

You should see the following plot which is similar to the previous Simulink Scope

output.

The modeling information is continued below:

Simulink Modeling Tutorial

Train system

Free body diagram and Newton's law

Model Construction

Running the Model

Obtaining MATLABModel

In Simulink, it is very straightforward to represent a physical system or a model. Ingeneral, a dynamic system can be constructed from just basic physical laws. We will

demonstrate through an example.
http://e/ctmssimulinkmodel%22%20lhttp://e/ctmssimulinkmodel%22%20lhttp://e/ctmssimulinkmodel%22%20lhttp://e/ctmssimulinkmodel%22%20lhttp://e/ctmssimulinkmodel%22%20lhttp://e/ctmssimulinkmodel%22%20lhttp://e/ctmssimulinkmodel%22%20lhttp://e/ctmssimulinkmodel%22%20lhttp://e/ctmssimulinkmodel%22%20lhttp://e/ctmssimulinkmodel%22%20lhttp://e/ctmssimulinkmodel%22%20lhttp://e/ctmssimulinkmodel%22%20l


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Train system

In this example, we will consider a toy train consisting of an engine and a car. Assumingthat the train only travels in one direction, we want to apply control to the train so that it

has a smooth start-up and stop, along with a constant-speed ride.

The mass of the engine and the car will be represented by M1 and M2, respectively. The

two are held together by a spring, which has the stiffness coefficient of k. F represents the

force applied by the engine, and the Greek letter, mu (which will also be represented by

the letter u), represents the coefficient of rolling friction.

Free body diagram and Newton's law

The system can be represented by following Free Body Diagrams.

From Newton's law, you know that the sum of forces acting on a mass equals the masstimes its acceleration. In this case, the forces acting on M1 are the spring, the friction and

the force applied by the engine. The forces acting on M2 are the spring and the friction.In the vertical direction, the gravitational force is canceled by the normal force applied by

the ground, so that there will be no acceleration in the vertical direction. We will begin to

construct the model simply from the expressions:

Sum( f or ces_on_M1) =M1*x1' 'Sum( f or ces_on_M1) =M1*x1' '

Constructing The Model

This set of system equations can now be represented graphically, without further

manipulation. First, we will construct two copies (one for each mass) of the expressions

sum_F=Ma or a=1/M*sum_F. Open a new model window, and drag two Sum blocks

(from the Linear library), one above the other. Label these Sum blocks "Sum_F1" and"Sum_F2".


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The outputs of each of these Sum blocks represents the sum of the forces acting on eachmass. Multiplying by 1/M will give us the acceleration. Drag two Gain blocks into your

model and attach each one with a line to the outputs of the Sum blocks.

These Gain blocks should contain 1/M for each of the masses. We will be taking these

variable as M1 and M2 from the MATLABenvironment, so we can just enter the variable

in the Gain blocks. Double-click on the upper Gain block and enter the following into the

Gain field.

1/ M1

Similarly, change the second Gain block to the following.1/ M2

Now, you will notice that the gains did not appear in the Gain blocks, and just "-K-"

shows up. This is because the blocks are two small on the screen to show 1/M2 inside thetriangle. The blocks can be resized so that the actual gain can be seen. To resize a block,


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select it by clicking on it once. Small squares will appear at the corners. Drag one of

these squares to stretch the block.

When the Gain blocks are of sufficient size to display the actual gains, re-align them withthe signal line output from the Sum blocks. Also, label these two Gain blocks "a1" and

"a2".

The outputs of these gain blocks are the accelerations of each of the masses. We are

interested in both the velocities and the positions of the masses. Since velocity is theintegral of acceleration, and position is the integral of velocity, we can generate these

signals using integrator blocks. Drag two integrator blocks into your model for each of

the two accelerations. Connect them with lines in two chains as shown below. Label theseintegrators "v1", "x1", "v2", and "x2" since these are the signals these integrators will

generate.


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Now, drag two Scopes from the Sinks library into your model and connect them to theoutputs of these integrators. Label them "View_x1" and "View_x2".

Now we are ready to add in the forces acting on each mass. First, you need to adjust theinputs on each Sum block to represent the proper number (we will worry about the sign

later) of forces. There are a total of 3 forces acting on M1, so change the Sum_F1 block's

dialog box entry to:

+++


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There are only 2 forces acting on M2, so we can leave Sum_F1 alone for now.

The first force acting on M1 is just the input force, F. Drag a Signal Generator block from

the Sources library and connect it to the uppermost input of the Sum_F1 block. Label theSignal Generator "F".

The next force acting on M1 is the friction force. This force is equal to:F_f r i ct i on_1=mu*g*M1*v1

To generate this force, we can tap off the velocity signal and multiply by a gain,mu*g*M1. Drag a Gain block into your model window. Tap off the line coming from the

v1 integrator and connect it to the input of the Gain block (draw this line in several stepsif necessary). Connect the output of the Gain block to the second input of Sum_F1.

Change the gain of this gain block to the following.mu*g*M1


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Resize the Gain block to display the gain and label the gain block Friction_1.

This force, however, acts in the negativex1-direction. Therefore, it must come into the

Sum_F1 block with negativesign. Change the list of signs of Sum_F1 to+- +

The last force acting on M1 is the spring force between masses. This is equal to:k*(x1- x2)

First, we need to generate (x1-x2) which we can then multiply by k to generate the force.Drag a Sum block below the rest of your model. Label it "(x1-x2)" and change its list ofsigns to

- +

Since this summation comes from right to left, we need to flip the block around. Select

the bloc by single-clicking on it and select Flipfrom the Formatmenu (or hit Ctrl-F).

You should see the following.


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Now, tap off the x2 signal and connect it to the negative input of the (x1-x2) Sum block.Tap off the x1 signal and connect it to the positive input. This will cause the lines to

cross. Lines may cross, but they are only actually connected where a small block appears(such as at a tap point).

Now, we can multiply this position difference by the spring constant to generate the

spring force. Drag a Gain block into your model to the left of the Sum blocks. Change it's

value to k and label it "spring". Connect the output of the (x1-x2) block to the input of thespring block, and the output of the spring block to the third input of Sum_F1. Change the

third sign of Sum_F1 to negative (use +--).


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Now, we can apply forces to M2. For the first force, we will use the same spring force wejust generated, except that it adds in with positive sign. Simply tap off the output of the

spring block and connect it to the first input of Sum_F2.

The last force to add in the the friction on M2. This is done in the exact same manner as

the friction on M1, tapping off v2, multiplying by a gain of mu*g*M2 and adding to

Sum_F2 with negative sign. After constructing this, you should have the following.


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Now the model is complete. We simply need to supply the proper input and view theproper output. The input of the system will be the force, F, provided by the engine. We

already have placed the function generator at the input. The output of the system will bethe velocity of the engine. Drag a Scope block from the Sinks block library into your

model. Tap a line off the output of the "v1" integrator block to view the output. Label the

scope "View_v1".

Now, the model is complete. Save your model in any file you like. You can download thecompleted model here.

Running the Model

Before running the model, we need to assign numerical values to each of the variable

used in the model. For the train system, let
http://e/ctmssimulinkmodeltrain.mdlhttp://e/ctmssimulinkmodeltrain.mdl


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M1 = 1 kg M2 = 0.5 kg k = 1 N/sec F= 1 N u = 0.002 sec/m

g = 9.8 m/s^2

Create an new m-file and enter the following commands.

M1=1;M2=0. 5;k=1;F=1;mu=0. 002;g=9. 8;

Execute your m-file to define these values. Simulink will recognize MATLAB

variable foruse in the model.

Now, we need to give an appropriate input to the engine. Double-click on the functiongenerator (F block). Select a square wave with frequency .001Hz and amplitude -1

(positive amplitude steps negative before stepping positive).

The last step before running the simulation is to select an appropriate simulation time. To

view one cycle of the .001Hz square wave, we should simulate for 1000 seconds. Select

Parametersfrom the Simulationmenu and change the Stop Time field to 1000. Closethe dialog box.

Now, run the simulation and open the View_v1 scope to examine the velocity output (hit

autoscale). The input was a square wave with two steps, one positive and one negative.

Physically, this means the engine first went forward, then in reverse. The velocity output


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reflects this.

Obtaining MATLABModel

We can now extract a MATLABmodel (state-space or transfer function) from out

simulink model. In order to do this, delete the View_v1 scope and put an Out Block(from the Connections library) in its place. Also, delete the F function generator block

and put an In Block (from the Connections library) in its place. The in and out blocks

define the input and output of the system we would like to extract. For a detaileddescription of this process and other ways of integrating MATLABwith Simulink, click

here.

Save this model as train2.mdlor download our version here. Now, we can extract the

model into MATLAB. Enter the following command at the MATLABcommand window toextract a state-space model.

[ A, B, C, D] =l i nmod( ' t r ai n2' )
http://e/ctmssimulinkbasicimatlab.htmhttp://e/ctmssimulinkmodeltrain2.mdlhttp://e/ctmssimulinkmodeltrain2.mdlhttp://e/ctmssimulinkbasicimatlab.htm


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Date post:	03-Jun-2018
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